IMO, except for some college radio stations, and LPFM's, you won't find many DJ's/air talent playing CD's in the studio these days. 99% of music at commercial pop/rock/hip hop and classical radio stations is now on hard drive, and has been for almost decades now, in an automation system. Actually, at this point in time, it's getting harder and harder to find high quality professional (balanced output, highly rugged, remote startable, etc.) single play CD players for broadcast use (I don't consider Numark and Stanton CD players high quality). I feel sorry for stations that still heavily rely on CD players (and have built up CD libraries of 30,000 + CDs), and won't be able to replace the players in years to come (I know of some of these stations).
Getting back to WQXR, they are very tight in morning drive, as compared to most other classical radio stations. The morning host rarely allows any space (seconds of dead air) between intro-ing a classical piece, and him/her playing it (yes, this could be considered live assist, as the WQXR air talent, when not voice-tracked, puts the automation system in live assist, and manipulate {"running"} the board themselves, pausing the automation system when a live break is needed). I'm 99% sure the M-F morning WQXR host is live, and so is his news person. During the lockdown of the Pandemic, many WQXR hosts were doing their shows (usually live), from their homes or apartments. Many times during the morning show, you could hear sirens from the street, in the background, when the host had his mic open during a break. A few times the WQXR morning host even pointed this out. Across the board (as in 99% of music radio stations), most of the air talent that was relegated to a home studio environment during the Pandemic, is now back in the broadcast studio. WFMT's air talent for example, is live most times 6A-Midnight, Monday through Sunday. This is not the case at most classical radio stations.